Falconer's book [1]}, [2]}, and [3]} contain all relevant information on fractal dimensions we need; especially the two latter of them are designed for dynamical needs. One can find the definition of Hausdorff dimension in Section 3
and we recall that the Hausdorff dimension of a set \(E\)  will be denoted by \(\text{{\rm HD}}(E)\) . Many results on fractal dimensions for meromorphic functions have been obtained by several
authors, the interested reader can find an overview of them in the survey [4]} by Stallard.
